Question: Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x-4}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{4x^3-14x^2-7x-4}{x-4}=$
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} 4x^2+2x+1 \\ x-4|\overline{4x^3-14x^2-7x-4} \\ \mathllap{-(}\underline{4x^3-16x^2\phantom{-7x-4}\rlap )} \\ 2x^2-7x-4 \\ \mathllap{-(}\underline{2x^2-8x\phantom{-4}\rlap )} \\ x-4 \\ \mathllap{-(}\underline{x-4\rlap )} \\ 0 \end{array}$ We found that the quotient is $4x^2+2x+1$ and the remainder is $0$, which means the answer is simply a polynomial (no expression of the form $\dfrac{k}{x-4}$ ). $\dfrac{4x^3-14x^2-7x-4}{x-4}=4x^2+2x+1$